Invariance principles for absolutely regular empirical processes
Doukhan, P. ; Massart, P. ; Rio, E.
Annales de l'I.H.P. Probabilités et statistiques, Tome 31 (1995), p. 393-427 / Harvested from Numdam
@article{AIHPB_1995__31_2_393_0,
     author = {Doukhan, Paul and Massart, Pascal and Rio, E.},
     title = {Invariance principles for absolutely regular empirical processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {31},
     year = {1995},
     pages = {393-427},
     mrnumber = {1324814},
     zbl = {0817.60028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1995__31_2_393_0}
}
Doukhan, P.; Massart, P.; Rio, E. Invariance principles for absolutely regular empirical processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 31 (1995) pp. 393-427. http://gdmltest.u-ga.fr/item/AIHPB_1995__31_2_393_0/

N.T. Andersen, E. Giné, M. Ossiander and J. Zinn, The central limit theorem and the law of iterated logarithm for empirical processes under local conditions, Probab. Th. Rel. Fields, Vol. 77, 1988, pp. 271-305. | MR 927241 | Zbl 0618.60022

W.K. Andrews and D. Pollard, An introduction to functional central limit theorems for dependent stochastic processes, Inst. Stat. review, Vol. 62, 1994, pp. 119-132. | Zbl 0834.60033

M.A. Arcones and B. Yu, Central limit theorems for empirical and U-processes of stationary mixing sequences, J. Theoret. Prob., Vol. 7, 1994, pp. 47-71. | MR 1256391 | Zbl 0786.60028

P. Bártfai, Über die Entfemung de Irrfahrtswege, Studia Sci. Math. Hungar, Vol. 1, 1970, pp. 161-168. | MR 215377

R.F. Bass, Law of the iterated logarithm for set-indexed partial sum processes with finite variance, Z. Warsch. verw. Gebiete, Vol. 70, 1985, pp. 591-608. | MR 807339 | Zbl 0575.60034

H.C.P. Berbee, Random walks with stationary increments and renewal theory, Math. Cent. Tracts, Amsterdam, 1979. | MR 547109 | Zbl 0443.60083

I. Berkes and W. Phillip, An almost sure invariance principle for the empirical distribution of mixing random variables, Z. Wahrsch. Verw. Gebiete, Vol. 41, 1977, pp. 115-137. | MR 464344 | Zbl 0349.60026

E. Bolthausen, Weak convergence of an empirical process indexed by the closed convex subsets of I2, Z. Wahrsch. Verw. Gebiete, Vol. 43, 1978, pp. 173-181. | MR 499430 | Zbl 0364.60033

R.C. Bradley, Basic properties of strong mixing conditions, in Dependence in probability and statistics a survey of recent results, Oberwolfach 1985, Birkhäuser, 1986. | MR 899990 | Zbl 0603.60034

Yu. A. Davydov, Mixing conditions for Markov chains, Theory Probab. Appl., Vol. 28, 1973, pp. 313-328. | Zbl 0297.60031

S. Dhompongsa, A note on the almost sure approximation of empirical process of weakly dependent random vectors, Yokohama math. J., Vol. 32, 1984, pp. 113-121. | MR 772909 | Zbl 0556.60015

M. Donsker, Justification and extension of Doob's heuristic approach to the Kolmogorov-Smimov's theorems, Ann. Math. Stat., Vol. 23, 1952, pp. 277-281. | MR 47288 | Zbl 0046.35103

J.L. Doob, Stochastic Processes, Wiley, New-York, 1953. | MR 58896 | Zbl 0053.26802

P. Doukhan, Mixing: properties and examples, Lecture notes in Statistics 85, Springer, 1994. | MR 1312160 | Zbl 0801.60027

P. Doukhan, J. León and F. Portal, Principe d'invariance faible pour la mesure empirique d'une suite de variables aléatoires dépendantes, Probab. Th. rel. fields, Vol. 76, 1987, pp. 51-70. | MR 899444 | Zbl 0596.60037

P. Doukhan, P. Massart and E. Rio, The functional central limit theorem for strongly mixing processes, Ann. Inst. H. Poincaré, Probab. Stat., Vol. 30, 1994, pp. 63-82. | Numdam | MR 1262892 | Zbl 0790.60037

R.M. Dudley, Weak convergence of probabilities on nonseparable metric spaces and empirical measures on Euclidean spaces, Illinois J. Math., Vol. 10, 1966, pp. 109-126. | MR 185641 | Zbl 0178.52502

R.M. Dudley, The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, J. Functional Analysis, Vol. 1, 1967, pp. 290-330. | MR 220340 | Zbl 0188.20502

R.M. Dudley, Central limit theorems for empirical measures, Ann. Probab., Vol. 6, 1978, pp. 899-929. | MR 512411 | Zbl 0404.60016

R.M. Dudley, A course on empirical processes. Ecole d'été de probabilités de Saint-Flour XII-1982. Lectures Notes in Math., Vol. 1097, Springer, Berlin, 1984, pp. 1-142. | MR 876079 | Zbl 0554.60029

M. Fréchet, Sur les tableaux de corrélation dont les marges sont données, Annales de l'université de Lyon, Sciences, section A, Vol. 14, 1951, pp. 53-77. | MR 49518 | Zbl 0045.22905

M. Fréchet, Sur la distance de deux lois de probabilité, C. R. Acad. Sci. Paris, Vol. 244, No. 6, 1957, pp. 689-692. | MR 83210 | Zbl 0077.33007

E. Giné and J. Zinn, Some limit theorems for empirical processes, Ann. Probab., Vol. 12, 1984, pp. 929-989. | MR 757767 | Zbl 0553.60037

N. Herrndorf, A functional central limit theorem for strongly mixing sequences of random variables, Z. Wahr. Verv. Gebiete, Vol. 69, 1985, pp. 541-550. | MR 791910 | Zbl 0558.60032

I.A. Ibragimov, Some limit theorems for stationary processes, Theory Probab. Appl., Vol. 7, 1962, pp. 349-382. | MR 148125 | Zbl 0119.14204

V.I. Kolchinskii, On the central limit theorem for empirical measures (In Russian), Teor. vero. i. mat. stat. (Kiev), Vol. 24, 1981, pp. 63-75. | MR 628431 | Zbl 0478.60039

A.N. Kolmogorov and Y.A. Rozanov, On the strong mixing conditions for stationary gaussian sequences, Theory Probab. Appl., Vol. 5, 1960, pp. 204-207. | Zbl 0106.12005

P. Massart, Invariance principles for empirical processes: the weakly dependent case, Quelques problèmes de vitesse de convergence pour des mesures empiriques. Thèse d'Etat, Université de Paris-Sud, 1987.

A. Mokkadem, Propriétés de mélange des modèles autorégressifs polynomiaux, Ann. Inst. Henri Poincaré, Probab. Stat., Vol. 26, 1990, pp. 219-260. | Numdam | MR 1063750 | Zbl 0706.60040

M. Ossiander, A central limit theorem under metric entropy with L2-bracketing, Ann. Probab., Vol. 15, 1987, pp. 897-919. | MR 893905 | Zbl 0665.60036

W. Philipp and L. Pinzur, Almost sure approximation theorems for the multivariate empirical processes, Z. Wahr. Verv. Gebiete, Ser. A, Vol. 54, 1980, pp. 1-13. | MR 595473 | Zbl 0424.60030

D. Pollard, A central limit theorems for empirical processes, J. Aust. Math. Soc., Vol. 33, 1982, pp. 235-248. | MR 668445 | Zbl 0504.60023

D. Pollard, Convergence of stochastic processes, Springer, Berlin, 1984. | MR 762984 | Zbl 0544.60045

D. Pollard, Empirical processes: theory and applications, NSF-CBMS Regional Conference Series in Probability and Statistics IMS-ASA, Hayward-Alexandria, 1990. | MR 1089429 | Zbl 0741.60001

P. Révész, Three theorems of multivariate empirical process. Lectures Notes in Math., Vol. 566, Springer, Berlin, 1976, pp. 106-126. | MR 436295 | Zbl 0354.60007

E. Rio, Covariance inequalities for strongly mixing processes, Ann. Int. H. Poincaré, Prob. Stat., Vol. 29, 1993, pp. 587-597. | Numdam | MR 1251142 | Zbl 0798.60027

M. Rosenblatt, A central limit theorem and a strong mixing condition, Proc. Nat. Ac. Sc. U.S.A., Vol. 42, 1956, pp. 43-47. | MR 74711 | Zbl 0070.13804

A.V. Skorohod, On a representation of random variables, Theory Probab. Appl., Vol. 21, 1976, pp. 628-632. | MR 428369 | Zbl 0362.60004

T.G. Sun, Ph. D. dissertation, Dept of Mathematics, Univ. of Washington, Seattle, 1976.

M. Talagrand, Regularity of Gaussian processes, Acta Math., Vol. 159, 1987, pp. 99-149. | MR 906527 | Zbl 0712.60044

V.A. Volkonskii and Y.A. Rozanov, Some limit theorems for random functions, Part I, Theory Probab. Appl., Vol. 4, 1959, pp. 178-197. | MR 121856 | Zbl 0092.33502

K. Yoshihara, Note on an almost sure invariance principle for some empirical processes, Yokohama math. J., Vol. 27, 1979, pp. 105-110. | MR 560618 | Zbl 0418.60037